Timo Niroma:
One possible explanation for the cyclicity in the Sun.

Sunspot cycles and supercycles and their tentative causes.

These pages have their origin in calculations made in 1988-1991,
The calculations and hypotheses have been redone beginning from June 1998 to December 1998 and have been put to Internet that same period. There is annually added information after that and now in 2009 there is going on a greater update because of the cycle 23 is ending.














The Sun at the moment (Soho): Click here


***************************************************************
PART 1. INTRODUCTION
***************************************************************
  • ALERT 31.10.2007: A probable new superminimum.

  • Forewords.
  • A speculative hypothesis to explain the Jupiter effect.


  • 1.1. Variation in the length of the sunspot cycles.
  • 1.2. How do the sunspot minima relate to the Jovian perihelion?
  • 1.3. The relation of the length of the cycle to its magnitude


  • PART 2: Jupiter and the Sun
  • - Average sunspot magnitude during 19 Jovian years 1762-1987.
    - Is the Jovian effect real or an artifact?
    - How many Jovian years are needed for the effect to show up?

  • PART 3: Minima, maxima and medians of the sunspots
  • - Magnitude minima.
    - Magnitude maxima.
    - Medians and quartiles.
    - The perihelian stability.

  • PART 4: From basic cycles to supercycles
  • - How long is the 11-year cycle?
    - The rules of Schove interpreted.
    - The Precambrian Elatina formation.
    - The Gleissberg cycle.

  • PART 5. The 200-year sunspot cycle is also a weather cycle.
  • - A 2000-year historical perspective.
    -- The Roman Empire and its demise.
    -- The Mayan Classic Period.
    -- When the Nile froze in 829 AD.
    -- Why is it Iceland and Greenland and not vice versa?
    -- Tambora did not cause it.
    -- The spotless century 200 AD.
    -- The recent warming caused by Sun.
    -- The 200-year weather pattern.
    - An autocorrelation analysis.
    -- Three variants of 200 years.
    -- The basic cycle length.
    -- The Gleissberg cycle put into place.
    - Some studies showing a 200-year cyclicity.
    - The periods of Cole.

  • PART 6: Searching supercycles by smoothing.


  • - Smoothing sunspot averages in 1768-1992 by one sunspot cycle.
    - Smoothing by the Hale cycle.
    - Smoothing by the Gleissberg cycle.
    - Double smoothing.
    - Omitting minima or taking into account only the active parts of the cycle.




  • PART 7: Summary of supercycles and a hypercycle of 2289 years.
  • - Short supercycles.
    - Supercycles from 250 years to a hypercycle of 2289 years.
    - The long-range change in magnitudes.
    - Stuiver-Braziunas analysis: 9000 years?

  • PART 8: Organizing the cycles into a web.
















  • ******************************************************************
    ALERT: A PROBABLE NEW SUPERMINIMUM
    ******************************************************************

    Original alert 31.10.2007

    Latest update 23.06.2009

    According to my theory about Jovian effect on sunspots, based on facts measured since 1700 and estimated since 1500 (Schove)
    - The Jupiter perihelion and sunspot minimum never coincide and the nearing perihelion in 2011 will slow the rise of the height of sunspot cycle, as now is happening to the cycle 24.
    - The Gleissberg cycle almost reached its lower limit, which is 72 years in 2005.
    --- In fact this low it has not been ever after the Maunder minimum.
    --- So it must go up, the short cycles of the 20th century has created a debt that must be paid.
    --- This means lower cycles and if the past is a good predictor, colder times on Earth.

    The last decent sunspots belonging to cycle 23 appeared in July 2008. From August to September 2008 the Sun hibernated. In October and November the cycle 24 showed its first decent spots. In December 2008 the Sun again began to hibernate if we count only the sunspots. At the same time there however began a rise of corrected (to 1-AU-distance) 10.7 cm flux since December 2008. In May/June it seems that the hibernation is over (at least for the time). The slow rise of the cycle 24 may be due to Livingston-Penn phenomenon of the spot's decreasing magnetism since at least 1990 which may delay the ongoing cycle switch. It seems that the time period from January to April 2009 has all the time being a preparation of cycle 24. We just did not in the 20th century get accustomed to look so quiet a period.

    This prolonged minimum and the delay of the cycle 24 mean that the cycle 24 will be very low, a new Maunder minimum seems possible.

    The point is that a length that exceeds 12 years has always led to prolonged grand minimum (1798 Dalton minimum, 1856 Damon minimum). It is not known exactly how long the cycles before Maunder minimum were, but there seems to have been a minimum in 1620. This leads to 25 years for the two cycles 1620-1645 just before Maunder.

    This means a cooling for decades, at least for 30 years, but we cannot be sure we are on a course to a new LIA (Little Ice Age). A low Dalton is probable, but one can't be sure, there are too many indications of the solar magnetic field having a deep dive.

    (A sidestep: The rise of the CO2 in atmosphere from 0.03 to 0.04 % does not have any meaning in this play where the water vapour is far the greatest player. I am a statistician and this is a statistical study, but a remark for those, who urgently for years have asked me what I think about the physical link: The Earth's magnetic field is very sensible to variations in the solar magnetic field. This may have far more greater effects to Earth than just the aurorae or breakdown of man-made electrical grids. I find the Svensmark theory (2006) of cosmic rays oscillating to the rhythm of the Sun's magnetic field as the most promising. More cosmic rays leads to more clouds in the lower atmosphere, which cools the Earth. The CERN investigations in 2010 probably will settle the issue. As I understand it the water vapor is the most forceful greenhouse gas. Although in the beginning a positive feedback when the water vapor changes to clouds the feedback changes to negative thus keeping a balance, where a 0.01% rise can't have any discernible influence. If the water vapour feedback wouldn't in the end to change negative, the Earth would eons again lost its oceans. There are also indications that the UV spectrum of the solar radiation oscillates many times more than the visible part. A sizable drop in UV plus sizable drop in TSI (Total Solar Irradiation) plus sizable drop in the spots' magnetic power combined with on-going cycle switches with bottom values creates thus an environment where all preconditions for a Maunder Minimum type minimum are set.)

    *******************************************************************


    Forewords

    Ever since Heinrich Schwabe and Rudolf Wolf in the years 1843-51 calculated that the amount of the sunspots varied in periods of about 11 years, there has been speculations that some planets, perhaps Jupiter in the first place, have something to do with the periodicity. Speculations are based not only on the fact that the orbital period of the planet Jupiter - 11.86 years - is near the generally accepted value for the sunspot period - 11.1 years - but also on the facts that there are no known mechanism that regulates the sunspot activity and that Jupiter is, besides the Sun, the only body in our planetary system whose output of energy is greater than the input.

    When the planetary effects have been searched as a cause for sunspots, a gravitational effect is mostly assumed. My theory is purely statistical so it does not necessitate a theory about the physical background. But still one can make some speculations. Evidence strongly suggests that the sunspots have a clear electromagnetic nature. The solar system baths in the electromagnetic field of the Sun. Nasa announced in 2008 that there are some kind of electromagnetic "ropes" between the Sun and possible all the planets that have an electromagnetic field of their own (such as Earth and Jupiter for example).

    I make a suggestion: The electromagnetic fields of Sun and Jupiter are partly intertwined, sometimes more, sometimes less during the nearly 12-year orbital revolution of Jupiter. Changes in eccentricity may then cause long-period changes in Sun's activity. And one thing we don't know: if the theory of everything combines gravity and electromagnetic forces the warping of space around Sun would really cause something extraordinary, like changes in the Sun's activity. One interesting thing is, that although the main effect of Jupiter seems to come via the perihelia of Jupiter, also the points where Jupiter crosses the plane of equator of the Sun, seem to have some effect.

    A speculative hypothesis to explain the Jupiter effect

    If we ignore the elliptical orbit of Jupiter around the Sun and replace it with a more easily grasped model, we can imagine Jupiter as approaching the Sun 5.93 years and then suddenly reverse the approach to escape for the next 5.93 years at the moment Jupiter is at its heliocentric perihelion. Now we see that we can imagine Jupiter's magnetosphere as approaching the Sun, intruding into it, warping it and finally intertwin with it, when Jupiter approaches the Sun. During the perihelion the direction and effect are suddenly reversed. As you see later, the statistical measurements show that sunspots in average get more scarce when Jupiter nears the Sun. At the perihelion the smoothed value has never exceeded 100 Wolfs since we have the monthly values from 1749.

    Besides during the perihelion, or at the moment of the reverse, the solar wind ceases for a day or two, causing the magnetosphere of Jupiter to expand enormously. If the Jupiter's reverse happens during the rise period of Sun's activity, it dampens the rise, causes the maximum of the ongoing cycle to be low or moderate and lengthens the cycle period.

    The question if the other planets have noticeable effect on the Sun, remains open. There are hints that they may have. I have however not studied them irrespective of Jupiter, but the Jupiter effect noticed does not deny that other planets could have some effect, albeit smaller than Jupiter.

    Still, the prevailing theory, the agreed-upon consensus amongst the astronomers seems to be against the idea that any planet could regulate the sunspot behaviour. We have no proved physical theory about how the influence would work. My study is a pure statistical theory and it shows interesting patterns. I leave to the physicists the arena to think any explanations, I only show statistical patterns and maybe sometimes speculate a little.

    1. Introduction

    1.1. Variation in the length of the sunspot cycles

    1.1.1. Two modes of cycle length distributions

    I shall begin by studying the distribution of the lengths of the sunspot cycles. Unfortunately there are only 23 cycles, beginning in 1745, a little more than 250 years, whose data are reliable enough to submit themselves to a statistical analysis. That is why they have in this stage only an introductory character. The analysis in the later chapters is mostly made using the monthly Wolf values. Then we get rid of the difficulty with the criteria of defining where a minimum really was this or that time and instead of 22 or 23 values we have nearly 3000 values.

    But even if we had enough values of the cycle lengths for a reliable statistical analysis, there is another difficulty that is inherent with the lengths: they are measured from a cycle minimum to the next minimum, but the definition of a cycle minimum is not based on any theory. It has been internationally agreed that the minimum is the month, whose smoothed Wolf number is the smallest. The smoothed values are calculated effectively as an average value of 13-month running means (actually as the average of two consecutive 12-month running means). In case this produces several minima, the number of spotless days per month is used for help.

    Now the situation has changed still more. The last minimum was so difficult to establish or the smoothed month seemed not to be the right one, that the scientists decided to use still more criteria to define when the minimum actually occurred. This leads to the curious situation that we have two minima for the beginning of cycle 23 and therefore two different lengths for the cycle 22.

    Let's look closer upon the difficulty: the twelve monthly Wolf values for the minimum year 1996 were: 10, 10, 10, 9, 8, 9, 8, 8, 8, 9, 10, 10. The old mathematical smoothing gives as the minimum month May (1996.4). But if we take the new criteria into account, the right month is October (1996.8). Because the beginning of the cycle 22 is calculated to be 1986.8, we get for the cycle 22 either a length of 9.6 or 10.0 years. But I have doubts even for the accuracy or rightness of this minimum. (I will discuss that later). However, when we make comparisons, we must use the same criteria for all. So in the next table I use the length calculated in the same way as the others or in this case 9.6 years. One exception I however make, because in one case the smoothed values do not solve the place of the minimum. This happened in 1809-1811 when there are more 0 Wolf months than the 13 ones used in the calculations.

    Even if we trusted the agreed-upon values as an approximation, we must give some room for inaccuracy. As a first approximation I estimate the accuracy of the lengths to be plus minus 0.2 years based on the inaccuracy of the Wolf estimates and the varying lengths of the months combined with the rotation period of the sun not exactly matching it and the use of one tenth of the year instead of the month plus the arbitrariness of the 13-month smoothing.

    The case of a questionable minimum mentioned above is the minimum which separates the cycles 5 and 6. There is in fact a clear separation, the year 1810 is the only totally spotless year since the regular observations began in 1749. The question is about the month of the minimum, because the number of months whose sunspot number is zero far exceeds the 13 months used when calculating the running means. The middle point used instead depends on whether we use as limits 0.0, 0.4 or some higher value (e.g. 10) or instead of using the middle point use smoothing by a greater value than 13 months. The generally used minimum is 1810.6, which uses the 0.0 limits. Other estimates give 1810.4 or 1810.5. So in all probability the length of the cycle 5 is estimated as too high and that of the cycle 6 as too low. I use here as the limiting value 0.4, because the descent and ascent to and from that value seem to be clear turning points in the activity. This gives a minimum date of 1810.4.

    TABLE 1. The sunspot cycle lengths since 1745.

    The second vertical lines mark the average sunspot period (11.07 years). The third double line marks the Jovian year (11.86 years). The first lines are a mirror of the Jovian line (10.2-10.3 years). Although 11.1 years seems to a mean of the cycle lengths, 10.3 years seems to be in top of the most common lengths (10.1-10.6 years). The lengths are based upon data calculated in Boulder, Colorado except the 1810 minimum. Otherwise the lengths are based on the 13 weighted month smoothed average. In a tie case the number of spotless days is used to break the tie. The length of the cycle 0 is tentative only.

    1. the number of the cycle
    2. the minimum as a tenth of the year
    3. the length of the cycle numerically
    4. the length of the cycle graphically (3 tenths added before and after)

    1.     2.   3. 4.
     0 1745.0 10.2 ------------??????????
     1 1755.2 11.3 ----------------|-|------o|o|oxooo 
     2 1766.5  9.0 oooxooo
     3 1775.5  9.2 --oooxooo
     4 1784.7 13.6 ----------------|-|-------|-|-------|-|------------>
     5 1798.3 12.1 ----------------|-|-------|-|------o|o|oxooo        
     6 1810.4 12.9 ----------------|-|-------|-|-------|-|------oooxooo   
     7 1823.3 10.6 ----------------|o|ooxooo
     8 1833.9  9.6 ------oooxooo
     9 1843.5 12.5 ----------------|-|-------|-|-------|-|--oooxooo
    10 1856.0 11.2 ----------------|-|-----oo|o|xooo
    11 1867.2 11.7 ----------------|-|-------|-|xxoooxo|o|o
    12 1878.9 10.7 ----------------|-|oooxooo
    13 1889.6 12.1 ----------------|-|-------|-|------o|o|oxooo
    14 1901.7 11.9 ----------------|-|-------|-|----ooo|x|ooo
    15 1913.6 10.0 ----------oooxoo|o|
    16 1923.6 10.2 ------------ooox|o|oo
    17 1933.8 10.4 --------------oo|o|xooo
    18 1944.2 10.1 -----------oooxo|o|o
    19 1954.3 10.6 ----------------|o|ooxooo
    20 1964.9 11.6 ----------------|-|-------|-|-oooxoo|o|
    21 1976.5 10.3 -------------ooo|x|ooo
    22 1986.8  9.6 ------oooxooo   
    23 1996.4 active part 12 years + minimum that may last 15 years.
    

    ****************************************************************

    Of the cycles 1-23
    - 12 are shorter than average
    - 2 (9%) may be of average length (cycles 1 and 10)
    - 9 are longer than average

    Of the longer cycles
    - 5 (22%) may have a length of 1 Jovian year (cycles 5, 11, 13, 14 and 20)
    - 4 are longer than 1 Jovian year (cycles 4, 6, 9, and possibly 23)

    Two things catch the eye. First thing is that only 2 or 9 % of the cycles seem to have the average length as their length. The lengths are either clearly longer or clearly shorter than the average length and there are two favoured lengths, 11.8-11.9 and 10.2-10.3 years.

    The other thing is that the long cycles are all old and the recent cycles are short. There has not been a longer than Jovian year cycle since the cycle 9 1843-1856 at least before the cycle 23 (1996-(2009?).

    7 of the 9 Jovian or longer cycles occupy the 19th century or its immediate vicinity.
    - Of the 11 cycles from 4 to 14 or from 1784 to 1913 7 or 64% belong to this category.
    - Of the 8 cycles from 15 to 22 or from 1913 to 1996 only 1 or 12.5% belongs to this category.
    - The cycle 23, which began in 1996, now may be the longest cycle since the cycle 9, which ended in 1856.

    On the other hand the long or Jovian period 1784-1913 contains no cycle in the category 10.2-10.3 years, which is so typical to the 20th century. All the 5 cycles 15-19 or in 1913-1964 plus the cycle 21 1976-1986 belong to this category. The cycle 22 seems to be a little shorter than other 20th century cycles, at least, if we rely on the conventional way of counting the lengths. Then it belongs to the category that holds the cycles 2, 3 and 8. The cycles following the short cycles 3 and 8 were followed by cycles that were longer than the Jovian cycle. The cycle 22 then follows the suit.

    The range of the cycles in the years 1745-1986 is from 9.0 to 13.6 years. If we count the frequency of aurorae we can go back to the year 1501. The aurorae follow so closely the frequency of sunspots that we can use them as an estimate of the sunspot cycles. This gives us as the lowest estimated value in the years 1501-1745 9.3 years and as the highest one 13.5 years. We can thus be confident that at least during the last half millennium the cycle length has not been below 9 years or higher than about 13 and half years (counted from minimum to minimum).

    How do these limits compare to Jovian years? 1.15 Jovyr is 13.6 in our calendar years. 0.75 Jovyrs is 8.9 calyrs. The shortest cycle is two thirds of the longest, or if we prefer, the longest cycle is one and a half times the shortest. Is this a coincidence or does it have some deeper meaning?

    In the following table I have put the cycle lengths into categories so that we can see the distribution more clearly and at the same time I have got rid of the false impression that the 0.1 years accuracy gives us. I selected as the interval for the classes 0.8 years, because it is the time between the average and the 10+ year cycle as well as the time difference between one Jovian year and the average cycle. As the middle category I selected the class that got the least number of hits or that gap around the average length.

    TABLE 2. The sunspot cycle lengths classified.

    x = the 7 cycles 1-7 or 1755-1833
    o = the 5 cycles 8-12 or 1833-1889
    v = the 10 cycles 13-22 or 1889-1996
    p = the cycle 23 or 1996-2009
    (prediction)

    length      no and kind of cycles
     8.4- 9.1 x 
     9.2- 9.9 xov
    10.0-10.7 xovvvvvv
    10.8-11.5 xo
    11.6-12.3 xovvv
    12.4-13.1 xop (p=prediction)
    13.2-13.9 x
    

    **********************************

    The cycles 1-7 in the years 1755-1833 are both evenly and broadly distributed so that every class gets one and only one hit. The cycles 8-12 in the years 1833-1889 are almost similarly divided except that the two extreme classes on both ends do not get a hit.

    The cycles 13-22 divide in two classes, the longer one has an average length of 11.87 years and the shorter one 10.17. If we leave cycle 22 out, we get an average length of 10.27 years. Thus we can hypothesize that the 20th century cycles have had only two possible lengths if we allow an accuracy of 0.4 years.

    CONCLUSION 1.

    ***************************************************************

    The sunspot lengths had during the years 1755-1889 an even and flat distribution containing the whole known range from 9 to 13.5 years.

    ***************************************************************

    CONCLUSION 2.

    ***************************************************************

    The sunspot lengths had during the years 1889-1996 only two possible values, either 10.2-10.3 years or 11.8-11.9 years. In Jovian years these are 0.86-0.87 and 1 years.

    ***************************************************************

    In the next table I have drawn lengths of the cycles so that the "official" value gets four points, the nearest value three points, the tenths of years whose distance is 0.2 years get two points and finally one point is given at the distance of 0.3 years. This should compensate for the inaccuracy of the values. For the years 5 and 6 I have used the calibrated values, for the cycle 22 the traditional value. The tentative cycle 0 (10.2 years) is added with a "o" notation.

    TABLE 3. A probability distribution of the sunspot lengths.

    yrs   points
     8.7 x
     8.8 xx
     8.9 xxxx
     9.0 xxxxxx
     9.1 xxxxxx
     9.2 xxxxxx                              
     9.3 xxxxxx                             
     9.4 xxxxxx                              
     9.5 xxxxxxx                           
     9.6 xxxxxxxx                           
     9.7 xxxxxxx                            
     9.8 xxxxxxx                              
     9.9 xxxxxxxxo                                
    10.0 xxxxxxxxxxoo                                  
    10.1 xxxxxxxxxxxxxooo                                 
    10.2 xxxxxxxxxxxxxxoooo                                
    10.3 xxxxxxxxxxxxxxxooo                               
    10.4 xxxxxxxxxxxxxxxoo                              
    10.5 xxxxxxxxxxxxxxo
    10.6 xxxxxxxxxxxxxx
    10.7 xxxxxxxxxxx
    10.8 xxxxxxx
    10.9 xxxxx
    11.0 xxxx
    11.1 xxxxx
    11.2 xxxxxxx
    11.3 xxxxxxxx 
    11.4 xxxxxxxx
    11.5 xxxxxxxx
    11.6 xxxxxxxxx
    11.7 xxxxxxxxx
    11.8 xxxxxxxxxx
    11.9 xxxxxxxxxxx
    12.0 xxxxxxxxxx
    12.1 xxxxxxxxxx
    12.2 xxxxxxxx
    12.3 xxxxxx   
    12.4 xxxxx                             
    12.5 xxxx   
    12.6 xxxx
    12.7 xxxx
    12.8 xxxx
    12.9 xxxx
    13.0 xxx                             
    13.1 xx                             
    13.2 x
    13.3 x
    13.4 xx
    13.5 xxx
    13.6 xxxx
    13.7 xxx
    13.8 xx
    13.9 x
    

    *****************************************************************

    The highest frequency goes to years 10.3-10.4. If we include the cycle 0, the highest frequency goes to years 10.2-10.3. If we use the alternative value for the cycle 22, we also get the high at 10.2-10.3 years. Actually the frequency distribution has two peaks. The other one, a little lower than the 10.2-10.4 year peak, is at the year 11.9 years, or 1 Jovian year. What is interesting is that the lowest frequency between these two peaks goes to the year 11.0 which is very close to the mean length of the sunspots.

    Remark the 0.8 year discrepancy that later in this study shows some importance:
    1. The short cycle: 10.28 years (reigning most of the 20th century).
    2. The mean length of the sunspots (1755-1996): 11.07 years.
    3. The long cycle: 11.86 (equals one Jovian year, four times in 1798-1913).

    CONCLUSION 3.

    ***************************************************************

    The mean sunspot length, 11.07 years, is not a preferred length for a single sunspot cycle. It is rather the mean of long cycles (1798-1913 = 11.5 years) and short cycles (1913-1986 = 10.5 years) or a combination of two modes of distribution.

    The century after the Maunder minimum (1700-1798) seems however had a cycle length of 10.9 years or near the mean.

    ***************************************************************


    1.1.2. How accurate is the estimated sunspot cycle length?

    There is no theoretical basis for using the 13-month smoothed values as the marker of the minimum. This has actualized with the difficulty of defining when the minimum between cycles 22 and 23 occurred. The Solar Cycle Prediction Panel decided in New Mexico in September 1997, that "when observations permit, a date selected as ... a cycle minimum ... is based in part on an average of the times when extremes are reached (1) in the monthly mean sunspot number, (2) in the smoothed monthly mean sunspot number, ... (3) in the monthly mean number of spot groups alone ... (4) the number of spotless days and (5) the frequency of occurrence of old and new cycle spot groups.

    First I inspect minima by varying the number of months used in smoothing (the above definition takes no explicit stand on the number). In the following table I have used the 10.7 cm flux instead of Wolf numbers, because they are more objective than the Wolf number, which after all is based on subjective observations. The flux is adjusted to 1 AU. Unfortunately the first whole year from which we have these radio fluxes is 1948, so that they cover only four whole sunspot periods, the periods 19-22. First I count the lengths of the cycles 19-21 by varying the smoothing periods and leave the cycle 22 for a later study.

    TABLE 4. The lengths of sunspot cycles 19-21 based on different smoothing periods

    running  method of      cycle19 cycle20 cycle21
    period    measurement
    
    13 mo    Wolf              10.6    11.6    10.3   
    
     9 mo    10.7 flux         10.3    11.8    10.5
    11 mo    10.7 flux         10.2    12.0    10.3
    13 mo    10.7 flux         10.4    11.7    10.3
    15 mo    10.7 flux         10.3    11.8    10.3
    

    **************************************************************

    We can see that the lengths vary as much as 0.4 years as we assumed in the previous tables. If we only replace Wolf by flux and keep the 13 month as the smoothing period, the cycle 19 is shortened from 10.6 to 10.4 and the cycle 20 lenghtened from 11.6 to 11.7 years. These are more in line with the long term trends from 1889 and the cycles 19 and 21 are practically of the same length. By increasing the smoothing period from 13 to 15 months, they are equal, 10.3 years and the cycle 20 has a length of one Jovian year.

    In the following table I have calculated lowest months as tenths of year of the four minima from which there exist 10.7 cm flux values. The purpose is to investigate the sharpness of the minima plus the possibility of several minima or a prolonged minimum.

    TABLE 5. The minima of sunspot cycles 19-22 based on the 5 lowest months

     method of    cycle19 cycle20 cycle21 cycle22 
    measurement
    
                   13 month running minimum
             Wolf  1954.3  1964.9  1976.5  1986.8
             flux  1954.3  1964.7  1976.4  1986.7
                   15 month running minimum
             flux  1954.3  1964.6  1976.4  1986.6
                   5 lowest smoothed months (as tenths of years)
             flux  1954.0  1964.5  1976.2  1986.0 begins
             flux  1954.4  1964.9  1976.5  1986.1 ends  
             flux                          1986.5 begins
             flux                          1986.7 ends  
    

    **************************************************************

    The minima of the minima 19, 20, and 21 are clear and relatively sharp, so there is not much room for speculation. Only the Wolf value of the cycle 20 minimum looks a little late. If we use the mid-month between the begin and end times instead of the average, we get for the cycle 19 a length of 10.5 years when the "official" Wolf value is 10.6 and the smoothed flux value is 10.3 or 10.4 years. For the cycle 20 we get 11.65 years, the official Wolf value being 11.6 and the smoothed flux value 11.7 or 11.8 years, all values being very near one Jovian year. The most probable lengths can be counted by using as the minima 1954.3, 1964.7 and 1976.4 giving lengths of 10.3 and 11.7 years for cycles 19 and 20, respectively.

    The case of the minimum of the cycle 22 is instead not so clear-cut. The "official" time of the minimum is calculated as 1986.8, but the first months of the year 1986 are almost equally low The monthly smoothed Wolf numbers for the year 1986 are 14, 13, 13, 14, 14, 14, 14, 13, 12, 13, 15, 16. (I would count the minimum as 1986.7 (8.5/12) but NGDC Boulder uses 1986.8 (9/12).) Now if we measure the length of the cycle 21 from the first minimum of the cycle 22, we get 9.6 years as the length for the cycle 21 instead of the "official" 10.3 years counted from the second minimum. Now we have a problem. If we be purely mathematical, the length of the cycle 21 is 10.3 years. But then we make a supposition that a minimum can only have one bottom value, which is not based on any theory. Thus we must take into account that this minimum had a secondary, albeit smaller, minimum 6-7 months or 0.5-0.6 years earlier. However for comparison reasons we must use the later date.

    The problem recurs during the minimum that ends the cycle 22 and begins the cycle 23, but maybe in a more dramatical fashion. I cite the "Summary Report of the Second Meeting of the Solar Cycle Prediction Panel" NSO/Sacramento, New Mexico: "The most problematic point discussed was the time of the cycle minimum. While the traditional numerical prescription as well as other measures of solar irradiance and activity agree that May, 1996, was the minimum smoothed month of the cycle, Karen Harvey noted that there are several factors that argue that this date is misleading as a fiducial for cycle 23 onset. In particular, no new cycle spots were observed before this month - a situation never before recorded.

    The date of minimum is expected to represent that time when new cycle activity becomes dominant; that is the new cycle should have been in progress as the old cycle declined, the minimum then marking the crossover. But for cycle 23, new cycle regions did not outnumber old cycle regions until December, 1996. The resurgence of activity in the months following May is due to old cycle regions. Another factor that indicates May is a misleading date is that the maximum number of spotless days occurred in September and October, 1996. ..." Thus "the Panel agreed that October, 1996, was the effective onset of cycle 23."

    NGDC, Boulder gives now two minima for the cycle 23 onset: May 1996 as the mathematical minimum and October 1996 as the consensus minimum. The first minimum gives for the cycle 22 a length of 9.6 years, the latter gives 10.0 years.

    I prefer the use of straight 15 month smoothing instead of the indirect 13 month smoothing, because it seems to give the most stabile and sensible point of minimum. When it is used, we get as the minimum month August 1996 (8.7), and the second lowest July and June. If we are using the 10.7 cm flux, we get minimum in July 1996 (the second lowest month is June). This gives some credence for the proposition that May really is too early. But in a similar way October is too late. It seems a little odd choice to nominate the last of the low months as the minimum of minimum. The 12 month list of the year 1996 is 12, 4, 9, 5, 6(*), 12, 9, 14(***), 2, 2(**), 19, 13 (Wolf) or 72, 70, 70, 70, 71(*), 72, 74(***), 74, 70, 69(**), 79, 75 (10.7 cm flux). * denotes the traditional method, ** the "consensus" method and *** my 15 month smoothing.

    Although the 15 month smoothing would suggest 1996.6 as the beginning for the cycle 23, for the reason to use equal criteria for all cycles, we must however use the date 1996.4 or otherwise change all the cycle minima. If we had used 15 month smoothing also for the earlier minimum, we would have 1986.6 as the beginning for the cycle 22, which would lead to 10 years. 15 months begins to be longest possible, because from 17 month onwards the bias caused by the asymmetric form of the cycle, slow descent but rapid rise, begins to take its toll. The method of the middle one of the five lowest months would also have led to 10.0 years. But maybe for consistency we must use the 13 month weighted average, or 1996.4, which leads to 9.6 years as the length of the cycle 22. We should not use different rules for one cycle than to the others.

    So we see here a deviation in 1996 from the bimodal pattern that otherwise reigned through the 20th century:


     method of    cycle20        cycle21        cycle22        cycle23
    measurement
    
                   13 month running minimum
             Wolf  1964.9 (11.6y) 1976.5 (10.3y) 1986.8 ( 9.6y) 1996.4
             flux  1964.7 (11.7y) 1976.4 (10.3y) 1986.7 ( 9.8y) 1996.5
                   15 month running minimum
             flux  1964.6 (11.8y) 1976.4 (10.2y) 1986.6 (10.0y) 1996.6
                   5 lowest smoothed months
                   (as tenths of years)
             flux  1964.5 begins  1976.2         1986.0 begins  1996.2
             flux  1964.9 ends    1976.5         1986.1 ends    1996.3 
             flux                                1986.5 begins  1996.5 
             flux                                1986.7 ends    1996.6
    



    1.1.3. Sunspot cycle length estimates extended to
    500 years by auroral numbers

    Now that we are convinced about the inaccuracy of the length of the sunspot cycles, even about the newest one, we possibly dare to use the aurorae for substitute to get more cycles. One particular reason for this is the Maunder minimum which occurred during the latter part of the 17th century. There were very few sunspots, during the last decade of that century virtually none.

    If we begin with the Jovian year cycles, according to Justin Schove, there may have been one in the 17th century, namely -10 or 1633-1645, the last one before the Maunder minimum. Now cycles 5 or 1798-1810 and 20 or 1964-1976 seem also to have been near one Jovian year long. Here we have something to begin with. The difference between these cycles is 15 and the length 165-166 years. 14 Jovian years is 166.07 calendar years. Are 1645, 1810 and 1976 synchpoint years having between them 15 sunspot cycles equalling 14 Jovian years and beginning a new phase in the Sun? 1645 started the cold and virtually spotless Maunder minimum. 1810 is in the middle of the cold Dalton minimum and is the last whole year without spots this far. 1976 ends a relatively cold period that is between two very warm periods with high and short cycles.

    One other thing seems also interesting. According to Schove, the period that ended the Maunder minimum, -4 from 1700 to 1713, seems to have had the maximum length observed or 13.5 years. The other cycles longer than one Jovian year were 4 (1784-1798), 6 (1810-1823) and 9 (1843- 1856). What is interesting is that these cycles or cycle groups (4-6) preceded anomalously short cycles. The cycle -5, during which was the coldest phase at least since 1600 in Europe, lasted only about 9 years. The cycles 2 and 3 both had a length of 9 years, but the following three cycles had a mean length of almost 13 years. The 12.5 years long cycle 9 was precided by the 9.5 years long cycle 8. Now there has been the cycle 22, whose length was 9.6 years. So cycle 23 should be long (12.5-15.5 years).

    This leads to an interesting speculation. If we rely on the Schove estimates based on aurorae, there has since 1500 been a tendency between intervals of 13 or 14 cycles to have the pairing either of one or two 9 to 9.5 years cycle plus immediately after them one 12.5-13.5 year cycle. Thus there are -19 and -18 about 1534-1554, the Maunder minimum minimum beginning in about 1690 (the cycle -5), and the cycle 8 in 1833-1843. And these cycles are always followed by one cycle whose length is longer than one Jovian year. So the cycles -17 (1554-1567), -4 (at the end of Maunder minimum 1700-1713) and 9 (1843-1856) belong to this category. The anomalous low cycles 5 and 6 are also preceded by the short cycles 2 and 3 and the long cycle 4 following also this schema thus proving that there are these pairs as well as Jovian length cycles (11, 13, 14) also outside these supercycles, but not vice versa: the supercycle still persists.

    Thus we have alternating 13 and 14 cycles between alternating one or two short cycles following long cycles. Short cycles: -19 and -18, (14), -5, (13) 8, (14) 22.

    SPECULATION 1.

    ***************************************************************

    Every 15 cycle has a length of 1 Jovian year. With intervals of 13 or 14 cycles there are 2 or 3 cycles such that 1 or 2 short cycles (less than 10 years) are followed one cycle that is longer than one Jovian year (12.5-13.5 years). Combined this gives 15*13.5 = 202.5, which is a supercycle (see later).

    ***************************************************************


    1.1.4. Length of several cycles combined

    Finally I will join consecutive cycles to see what kind of large scale variations there exist. I have next calculated the combined and average length of 4, 8, and 16 consecutive cycles using as the breakpoint the spotless year 1810. In the longer cycles I have used the Schove estimates based on aurorae.

    TABLE 6. Several cycles combined

    1. the cycles
    2. the years of minimum (from start of the first to the end of the last)
    3. the combined length
    4. the average length as Earth years

    4 cycles combined
    *****************

        1.        2.   3.   4. 
       
      2- 5 1766-1810 44.1 11.0      
      6- 9 1810-1856 45.4 11.4      
     10-13 1856-1901 45.7 11.4                       
     14-17 1901-1944 42.5 10.6                      
     18-21 1944-1986 42.5 10.6                     
    

    The difference of 0.8 years shows here clearly up between the 19th and 20th century.


    8 cycles combined
    *****************
          1.      2.    3.        4.    
    
     -2- 5 1723-1810 86-88 10.8-11.0 
      6-13 1810-1901  91.1      11.4       
     14-21 1901-1986  85.0      10.6       
    

    1810-1901 three of the eight cycles have a length of one Jovian year, none is near the 10.2-10.3 years. 1901-1986 only one of the eight cycles has the length of one Jovian year, all the others belong to the 10.2-10.3 year type. 200 years are needed to give the generally accepted value of the cycle length, a little over 11 years. The first 8 cycles is in this table show that there are at least three types of supercycles. The interesting question is did 1986 began a new supercycle, and if so, is it similar to the first one in this table, or a new, fourth type.


    16 cycles combined
    ******************
        1.        2.    3.    4.   
    
    -10- 5 1633-1810 176.9 11.06 sum inaccurate by +- one year
      6-21 1810-1986 176.1 11.01                           
    

    This is a most interesting table because it captures the Maunder minimum. Unfortunately the first supercycle is very inaccurate. Although 1633 seems to be the best choice for the minimum year, 1632 and 1634 are almost as possible. So this means a total length anywhere between 176 and 178 years. Could be the same as the latter, but still older records favor the mean of 11.07 years, so probably it had slightly longer cycles in average. On the other hand no-one can say if 16 cycles is any good indicator for a supercycle. The Jovian cycles seem to appear in 15 cycle intervals, and the pairs of short/long cycles in 13/14 cycle intervals. 14 cycles could give us an interesting pattern of 155 years: 310, 155, 77.5, 38.75, 19.375, 9.69 years (See later). Autocorrelation gives (this also more later) an about 210 year cycle. It is near 19 sunspot cycles and near 18 Jovian years. It has been increasing all since we have somewhat reliable dates for minima. And with one exception with about the same amount. The three most probable lengths from cycle 5 to cycle 24 are also depicted.

    TABLE 7. 19 cycles combined


    1. cycles
    2. years
    3. combined length
    4. change from the previous length
    5. average cycle length
    6. divided by 18 nears to one Jovian year (11.86)
    
       1.            2.    3.    4.   5.    6. 
                                    
     0-19 1745.0-1954.3 209.3      11.02 11.63
     1-20 1755.2-1964.9 209.7  0.4 11.04 11.65
     2-21 1766.5-1976.5 210.0  0.3 11.05 11.67
     3-22 1775.5-1986.8 211.3  1.3 11.12 11.74
     4-23 1784.7-1996.4 211.7  0.4 11.14 11.76
    
     5-24 1798.3-2008.8 210.5 -1.2 
     5-24 1798.3-2009.6 211.3 -0.4
     5-24 1798.3-2010.4 212.1  0.4 11.16 11.78
    

    ****************************************************************


    1.2. How do the sunspot minima relate to the Jovian perihelion?

    Now I make some questions. Because the mean sunspot length (11.07 years?) is shorter than the Jovian year (11.86 years) the distance between these two events should change in average 0.8 years or about 7% per Jovian year. But now we know, that the most preferred length is a 10.2-10.3 years. If we assume symmetricity around the mean length (at least it is not far), we can use the value 10.24 years, and thus we can expect that the average length should increase by 1.6 years or about 13.5% per Jovian year. This is interrupted sometimes by a cycle, whose length is 1 Jovian year. The first question is, do the perihelia of these Jovian years situate at some standard distance compared to the sunspot minima or are they randomly distributed? The other question is, how do the short/long cycles relate to Jovian perihelia.

    TABLE 8. Sunspot minima compared to Jovian perihelion

    1. the number of the sunspot period
    2. the year of Jupiter (the numbering is my own)
    3. the minimum time of the spots (the beginning of the cycle)
    4. the nearest Jovian perihelion
    5. the difference between sunspot minimum and Jovian perihelion
    6. the previous as a percentage of the Jovian year
    7. the change in the previous value
    8. remarks; the saying "over aphelion/perihelion" means that the minimum is situated on the different side of the aphelion/perihelion compared with its previous position

     1. 2.    3.     4.   5.   6.   7.        8.
     0  0 1745.0 1750.2 -5.2 -44% -14% slightly unreliable
    ----------------------------------over aphelion
     1  1 1755.2 1750.2  5.0  42%  -5%        
     2  2 1766.5 1762.1  4.4  37% -24% very short 
     3  3 1775.5 1774.0  1.5  13% -22% very short 
    ----------------------------------over perihelion
     4  4 1784.7 1785.8 -1.1  -9%  14% very long  
    ----------------------------------back     
     5  5 1798.3 1797.7  0.6   5%   2% very low, Jovian cycle
     6  6 1810.4 1809.6  0.8   7%   9% very low    
     7  7 1823.3 1821.4  1.9  16% -11%
     8  8 1833.9 1833.3  0.6   5% -18%
    ----------------------------------over perihelion
     9  9 1843.5 1845.1 -1.6 -13%   5%
    10 10 1856.0 1857.0 -1.0  -8%  -6%
    11 11 1867.2 1868.9 -1.7 -14%  -1% Jovian cycle    
    12 12 1878.9 1880.7 -1.8 -15% -10%
    13 13 1889.6 1892.6 -3.0 -25%   2% Jovian cycle    
    14 14 1901.7 1904.4 -2.7 -23%   -  Jovian cycle    
    15 15 1913.6 1916.3 -2.7 -23% -16%
    16 16 1923.6 1928.2 -4.6 -39% -14%
    ----------------------------------over aphelion
    17 16 1933.8 1928.2  5.6  47% -12%
    18 17 1944.2 1940.0  4.2  35% -15%
    19 18 1954.3 1951.9  2.4  20% -12% very high   
    20 19 1964.7 1963.8  0.9   8%   -  Jovian cycle    
    21 20 1976.5 1975.6  0.9   8% -14%
    ----------------------------------over perihelion
    22 21 1986.8 1987.5 -0.7  -6% -19%     
    23 22 1996.4 1999.4 -3.0 -25% (+5%...+18%)
     
    (24 23 2009? 2011.2 -0.8...-2.4% -7%...-20% prediction)
    
    

    *************************************************************

    Now I divide this perihelion dance, as I like to call it, into 5 periods and 3 types. Types are: A. Minima that occur when Jupiter is clearly nearer its aphelion than its perihelion. B. Minima that occur halfway or near halfway between perihelion and aphelion, i.e. at the distance of 2.4-3 years. C. Minima that occur when Jupiter is clearly nearer its perihelion than its aphelion, i.e. nearer than 2 years.

    Periods are as follows:

    Period 1. The 3 cycles from 0 to 2 (possibly including also the cycle -1). Type is A. This phase ends and following phase begins with the shortest known cycles (both are only 9 years long) as if the minimum had a great hurry to synchronize with the Jovian perihelion. SSN(max) around 100.

    Period 2. Consists of the next 10 cycles, from 3 to 12 (the first one began in 1775 and the last one in 1878). They all are type C. The minimum oscillates on both sides of the perihelion as if the perihelion had some attractive force. The first minimum is after, the second before, the next 4 again after and the last 4 before the perihelion. But one thing seems odd taking into account this attraction: none of the 10 minima occurs exactly at the perihelion. The cycles 3 and 4 hold the all time (since 1750) record of length difference (9 and 13.5 years) and the cycle 5 and 6 the all time (since the Maunder minimum) record of low spot number (both had a maximum of about 50 Wolfs) and between them is the only spotless year, 1810, since the Maunder minimum. The 10 cycles beginning during this phase has a mean length of 11.4 years. In summary, after 1749, this about 100 year period contains the shortest cycle, the longest cycle, the lowest cycle and the only spotless year. Sametime this 100 year period is the coldest period in Earth's climate since Maunder minimum, albeit it begins the warmest decade between the beginning of the Maunder Minimum (and possibly since 1400) and 1930, namely the 1770's. But it contains two cold minima, the Dalton minimum 1800-1820 and the Damon minimum 1840-1890.

    Period 3. Consists of the next 3 cycles, from 13 to 15 (the first one began in 1889 and the last one in 1913). They are of type B. The standstill halfway between perihelion and aphelion of cause means that the first two cycles of this period last 1 Jovian year. What caused the standstill at this point? One guess is that Jupiter intersects the plane of Sun's equator at 85.4 degrees from perihelion, which is 24% of the orbit. The quantum step made by cycle 12 (1878-1889) to get the tight grip of Jupiter to loosen a little only to get into a new trap was repeated by cycle 15 (1913-1923) which seemed to let the Sun to go its own speed without the grip of Jupiter. Small warming seen on Earth.

    Period 4. Consists of the next 3 cycles, from 16 to 18 (the first one began in 1923 and the last one in 1944). They are of type A. This phase contains a climate chage on Earth. 1923-1943, especially the 1930's was the warmest decade after the Maunder Minimum (just above the 1770's). What is interesting is that the previous phase that was type A (period 1) contained most probably 4 cycles and this one contains 3 cycles, whereas the type C period 2 contained 10 cycles. If we include the intermediary cycles 15 and 19, these five cycles all belong to the 10.3 year length category. So this connects together short cycles and freedom of Jupiter's grip (at least relatively) plus a warm Earth. In this sense the borderline cycle 19 could belong here, but because it was taken by Jupiter at its end, I rather situate it in the period 5.

    Period 5. Consists of the 4 cycles from 19 to 22. The beginning cycle 19 has an all time record (at least for 400 years) in height, 200 Wolfs. They are of type C. In one respect they behave in a similar attraction/avoidance way towards the Jovian perihelion as the C type cycles during period 2. Continuing the straight 10.3 year course began in 1913 by the cycle 15 would have caused the cycle 21 have its beginning minimum coincide with the Jovian perihelion. Instead the cycle 20 is prolonged to 1 Jovian year, so that the minimum of cycle 21 is postponed to occur almost a year after the perihelion. But the prolonged minimum beginning the cycle 22 occurs on its straight place as if nothing happened between, only that it occurs before the perihelion avoiding the collision of perihelion and minimum. Of course this avoidance had its price, the cycle 20 had to be a Jovian cycle to be able to avoid the collision. The cycle 23 that began in 1996, seems to start a new period.

    Altogether we have here 23 minima. 6 or 25% of them (0-2 or 1745-1766 and 16-18 or 1923- 1944) are of type A (on the aphelion side), 4 or 17% (13-15 and 23) are of type B (on the borderline), and 14 (3-12 or 1775-1878 and 19-22 or 1954-1986) or 58% are of type C (on the perihelion side). The distance between the two type A groups is 178 years or 15 Jovian years or 16 cycles. Type B is always before the perihelion, A and C may be on both sides. Type A is relatively free of planetary effects, types B and C are regulated more or less by Jupiter.

    DIFFERENT MOODS OF THE SUN
    =================================

    Every now and then there is a change in the mood of the Sun. Without going too far in the past I classify the most recent moods and their influence on our temperature as follows:

    1645-1699 Maunder Minimum, virtually no spots for 55 years. Increasing cold here on Earth, the coldest period at least in 400 years, the coldest decade was the 1690's. The longer the minimum lasted, the colder it there was. Justin Schove has found similar occasions in the centuries AD200 and AD600, no spots, very cold.

    1700-1766 Recovering Sun. Period begins most probably with a long cycle (13.5 years) and continues with only slightly disturbed cycles (estimated length 10.8 years).

    1766-1856 Restless Sun. Begins with two ultrashort cycles (about 9 years) which give for some years at least in the 1770's and at least in the Northern Europe temperatures achieved next only in the 1930's. According to 10Be measurements the 1770's is the least cloudy (most sunny) decade after 1700. Then follows the long cycle (13.6 years), which leads to Dalton Minimum (1798-1823, cold temperatures between 1801 and 1820). Oscillation continues to 1856.

    1856-1913 Jovian dominated Sun. Of the five cycles 4 have a length of one Jupiter year. Colder than after 1913 and partly during the latter part of the 1700's.

    1913-1996 Sun on its own. With one exception the cycles last as near 10.3 years as the circumstances allow (more appropriate measure methods would show this more clearly). Also the last cycle (cycle 22) is somehow disturbed in 1996. Warm, warmest in the 1930's and about 1985-2005. There are indications that the 1930ís were warmer than the later period. The 1945-1975 period equals quite well with the 1770ís at least in Uppsala, which I have used as a baseline on many occasions (not however after 1990 when UHI destroyed the continuity of one of the oldest and most reliable series of measurements (set up by Celsius himself in the first part of 1700ís)). The heavy spottiness (I mean SSN(max) about 160) gives the possibility to warm climate, but as above in many posts have clearly been shown, PDO (at least) modulates effectively the end result.

    1996- Sun is in trouble in thinking how to behave now (more seriously: different influences upon Sun conflict with each other at the moment). On Earth the changing mood is seen as cooling. Oceans began to cool after 2003, atmosphere from 2006.

    In the next table I have calculated the distance of the minimum from the Jovian perihelion and used the 0.8 year classification. I have omitted the sign and used the value as an absolute value to get the distance to the nearest perihelion regardless of whether the minimum or the perihelion was first. The maximum distance is of course half a Jovian year (5.93 years).

    TABLE 9. The distance between the sunspot minimum and the Jovian perihelion

    1. distance +- 0.4 years
    2. the cycles
    3. the cycles in time sequence

      1. / 2.                                        3.
       
    0.0                                                      PERIHELION 
    0.8 / 04 05 06 08 10 20 21 22      XXX X X         XXX           
    1.6 / 03 07 09 11 12 24?          X   X X XX           X?
    2.4 / 14 15 19 24?                          XX    X    X?        
    3.2 / 13 23                                   X       X        
    4.0 / 02 18                      X               X     
    4.8 / 01 16                     X              X             
    5.6 / 00 17                    X                X        APHELION 
    

    ***************************************************************

    The affection that the minimum shows to the Jovian perihelion seems very obvious, but it shows itself in a rather peculiar way: it avoids the exact time of the perihelion and prefers instead a distance of about 0.6-0.9 years.

    If we set the limit of the distance from the perihelion to +-2 years or +-17% or 1/3 of the Jovian year, 13 cycles are inside this region, whereas the remaining 2/3 Jovyrs or almost 8 calyrs contain only 11 cycles.

    To see the probability of chance producing this distribution, I made a binomial test. I tested the hypothesis that by chance 13 or more minima out of 24 are at a distance of 0.5-2.0 years of the perihelion.

    **************************************************************
    The probability of success = 0.25 ((2*(2.0-0.5))/11.86=0.253)
    Number of trials = 24 (minima)
    Number of successes = 13 (or more minima inside this region)
    Probability of success by chance = 0.0016 or 0.16% or 1 to 625.
    ***************************************************************

    So we can accept our hypothesis, that the phenomenon is real, with a probability of 99.84%.

    The last minimum which obeyed both the attraction and the avoidance was the one between cycles 20 and 21 (1976).

    In the following histogram I have drawn the absolute distances of minima from the Jovian perihelion calculated with accuracy limits as plus minus 0.2 years (i.e. five marks for each minimum). The vertical line represents the perihelion and the unit is one tenth of a year. Included is only the more populated area beginning with 3 years (3.2 with limit).

    TABLE 10. The most attractive distances between minima and perihelia

    0.0
    0.1
    0.2
    0.3
    0.4 xx
    0.5 xxxxx
    0.6 xxxxxxxxx
    0.7 xxxxxxxxxxx
    0.8 xxxxxxxxxxxx
    0.9 xxxxxxxxxxxx
    1.0 xxxxxxxxxx
    1.1 xxxxxxx
    1.2 xxx
    1.3 xx
    1.4 xxx
    1.5 xxxxxx
    1.6 xxxxxxxx
    1.7 xxxxxxxxx
    1.8 xxxxxxxx
    1.9 xxxxxx
    2.0 xxx
    2.1 x
    2.2 x
    2.3 xx
    2.4 xxx
    2.5 xxxx
    2.6 xxxxx
    2.7 xxxxxx
    2.8 xxxxxx
    2.9 xxxxxx
    3.0 xxxxxx
    3.1 xxxx
    3.2 xx
    

    **************************************************************

    It is easily seen that there are three favored distances from the perihelion: 0.7-0.9 years, 1.6-1.8 years and 2.4-3.0 years. The simultaneous hate and love of the perihelion is here clearly evident. 0.8 years is interestingly the distance from the mean of the sunspot cycle length both to the 10.3 year category lengths and the 1 Jovian years length (11.9 years). Similarly 1.6 years is exactly the difference between 1 Jovian year and most favored sunspot cycle length of 10.3 years. One lonely minimum (19) is at the distance of 2.4 years. The peak at 2.8-2.9 may have something to do with the Jovian orbit intersecting the plane of the Sun's equator 2.9 years before its perihelion. If that's true this distance occurs only before the perihelion, never after.

    **************************************************************

    CONCLUSION 4. The sunspot minima prefer an area around the Jovian perihelion

    At a distance beginning 0.5 years and ending 2 years before or after the Jovian perihelion is an area that attracts the sunspot minimum.

    CONCLUSION 5. The distance between minimum and perihelion is quantisized

    Taking into account the inaccuracies while measuring the exact location of the sunspot minima, we have good grounds to assume that inside 3 years before or after the Jovian perihelion there are only 3 possible distances that the minimum may occupy. The distances are 0.8, 1.6, (possibly also 2.4) and 2.8-2.9 years.

    CONCLUSION 6. The sunspot minimum and the Jovian perihelion never exactly meet

    If we take the last 250 years as representative, we can conclude that there never is an exact match of the sunspot minimum and the Jovian perihelion.

    ***************************************************************

    Finally I have drawn the perihelion dance of the minima as a graphical representation. The first column is the number of the beginning cycle, the column is the datum of the Jovian perihelion and X marks the minimum. The middle | marks the perihelion of Jupiter (that year in the second column), the side ones are the aphelia. Between the aphelia of Jovian years 15 and 16 are two minima. X is followed by 1-4 horizontal lines that mark the height of the maximum rounded to nearest 50 Wolfs (each line denoting 50 Wolfs).

    TABLE 11. THE MINIMA V. JOVIAN PERIHELION GRAPHICALLY

                Aph.              Perih.              Aph.
    Min Year/perih.       
     1    1750.2 |                  |              X--)|             
     2    1762.1 |                  |            X--)  |                 
     3    1774.0 |                  |    X---)         |
     4    1785.8 |               X---)                 |
     5    1797.7 |                  | X-)              |
     6    1809.6 |                  | X-)              |
     7    1821.4 |                  |     X-)          |
     8    1833.3 |                  | X---)            |
     9    1845.1 |             X---)|                  |
    10    1857.0 |               X--)                  |
    11    1868.9 |             X---)|                  | 
    12    1880.7 |             X-)  |                  | 
    13    1892.6 |         X--)     |                  |
    14    1904.4 |          X-)     |                  |
    15    1916.3 |          X--)    |                  |
    16/17 1928.2 |    X--)          |                X-|
    18    1940.0 |-)                |           X---)  |
    19    1951.9 |                  |      X----)      |
    20    1963.8 |                  |  X--)            |
    21    1975.6 |                  |  X---)           |
    22    1987.5 |               X---)                 |
    23    1999.4 |         X--)     |                  |
    24    2011.2 |         xxxxxxx? |                  |
    
    

    The shortening of the sunspot cycles beginning with the cycle 15 (1913-1923) is here clearly seen. The avoidance of the perihelion by the cycle 21 (the avoidance previously shown by cycles 4, 5, 6 and 8) is the only exception to the short cycles until the apparent lenghtening of cycle 23. The prediction is that we are now entering to long cycles similar to cycles 9 to 14 (1843-1913). The minima of the cycles 2 and 18 are nearly at even length after the perihelion, nearer the aphelion. The distance is 16 cycles or 178 years or 11.1 years per cycle. But the cycles 20 and 21 behave as the cycles 5, 6 and 8, the minimum is at the magical distance of 0.8 years after the perihelion. The first two cycles have a distance of 15 cycles or 166 years or 14 Jovian years. But the most recent minimum, that of cycle 23 occurs already halfway between the perihelion and the aphelion, at the point where Jupiter's orbit intersects the plane of Sun's equator. The previous minimum that did this occurred only 10 cycles or 107 years earlier.

    Every times the cycles begin at the same distance (about 1 Jovian year) there is cold on Earth: cycles 5-6 (Dalton minimum 1798-1823), cycles 9-14 (Damon minimum 1843-1913) and cycle 20 (cold war minimum 1964-1976). Looks like a new minimum is beginning with cycle 24. When the minima keep running (the cycles are short), there is warm: cycles 2-4 (1766-1795), cycles 7-8 (1823-1840), cycles 15-19 (1913-1961) and cycles 21-23 (1976-2005).

    EVERY OTHER CYCLE

                Aph.              Perih.              Aph.
    Min Year/perih.       
     2    1762.1 |                  |            X--)  |                 
     4    1785.8 |               X---)                 |
     6    1809.6 |                  | X-)              |
     8    1833.3 |                  | X---)            |
    10    1857.0 |               X--)                  |
    12    1880.7 |             X-)  |                  | 
    14    1904.4 |          X-)     |                  |
    16    1928.2 |    X--)          |                  |
    18    1940.0 |-)                |           X---)  |
    20    1963.8 |                  |  X--)            |
    22    1987.5 |               X---)                 |
    24    2011.2 |         xxxxxxx? |                  |
     
     
    

    The pairing of the cycles is now more clearly evident. Cycles 2 and 18, 6 and 20, and 10 and 22, and possibly 14 and 24 also seem to correspond each other. The cycle distance has diminished: 16 cycles, 14 cycles, 12 cycles and possibly 10 cycles. The cycles 2 to 4 were shorter than cycles 16 to 22, the nine-year cycles of the 18th century are exactly twice as short as the ten-year cycles in the 20th century if we count the distance from the Jovian perihelion. But this is true also internally: while the cycles 2 and 18 began at a distance of 4.3 years after the perihelion, the cycles 6 and 20 began 0.9 years after it or the distance diminished by 3.4 years in 4 and 2 cycles, respectively (0.8-0.9 years per cycle), but the corresponding distance from 6 to 10 and from 20 to 22 took half of the previous value, or 1.7 years when it crossed the perihelion. Both had a standstill and the previous one also a change of direction.

    But what happens next? How about the cycle 24? If the cycle 23 behaves according to the rules (every 13th/14th/15th, see earlier) that have prevailed since at least 1500, its length is about 12.5-13.5 years.

    SPECIAL LATER ADDITION. NASA: SOLAR WIND DISAPPEARED DURING THE JOVIAN PERIHELION IN 1999

    Space Science News by NASA (science.nasa.gov/newhome/headlines/ ast16dec99_1.htm) is titled "Solar cycle ups and downs continues to mystify scientists." I see no reason why they should mystify anybody. The Sun is much more variable than previously thought. That should not come as any surprise to scientists.

    According to the first prediction including 1999, made by National Geographical Data Center (NGDC) in Boulder, Colorado, in August 1997, was amazingly accurate. The prediction and actual numbers were (in smoothed Wolf numbers):

    year month pred. act.
    1998 Jun   60    62
    1998 Jul   63    65
    1998 Aug   66    68
    1998 Sep   69    70
    1998 Oct   72    71
    1998 Nov   76    73
    1998 Dec   79    78
    1999 Jan   82    83
    1999 Feb   84    85
    1999 Mar   87    84
    1999 Apr   89    85
    1999 May   92    90
    

    Only the stagnation from February to April 1999 was not seen in advance. Obviously, because the NGDC does not use one parameter, that according to my theory is essential. But later to that.

    However, in March 1998 NGDC made a big mistake. From August 1997 to February 1998 NGDC had said that "May 1996 marks Cycle 22's minimum and the onset of Cycle 23". Based on this premise, the predictions were excellent. But in March NGDC suddenly changed the time of the minimum. With NGDC's own words: "May 1996 marks Cycle 22's mathematical minimum. October 1996 marks the consensus Cycle 22 minimum which NGDC is now using." And has used since. It had a catastrophic effect on the prediction. June 1998 jumped from 60 to 73 (actual 62), November-December 1998 from 76-79 to 106-111 (actual 76-78) and May 1999 from 92 to 136 (actual 90). At the same time December 1999 jumped from 105 to 159 (year 2000 was not yet included).

    When the year 2000 prediction first appeared in June 1998, the maximum was predicted due to Mars 2000 with a value of nearly 160.

    What went wrong? We can easily see that this prediction will not be fulfilled. The Sun is is variable, but not that chaotic. The behavior of the Sun should be calculated mathematically, not by voting a consensus.

    According to my theory (personal.inet.fi/tiede/tilmari/sunspots.html) the smoothed sunspot Wolf value cannot exceed 90 during 20 months before Jupiter's perihelion, 100 exactly at the perihelion, and 110 10 months after the perihelion. Jupiter's perihelion was in May 1999. The actual Wolf value was near maximum allowable, 90.

    Now, when the influence of the choice of the time of minimum has continuously diminished and been replaced by the actual rise of the cycle 23, NGDC's predictions look again more reliable. The predicted value is 111-113 from February 2000 to Mars 2001, the peak being somewhere between Mars to November 2000. This sounds reasonable.

    But back to 1998-1999. The raw Wolf value which hovered between 60-90 in autumn 1998, stagnated to 62-69 from January to April 1999. Why? According to my theory this is the Jovian effect: when Jupiter nears its perihelion and the sunspot cycle is rising, it sets back to its prevailing minimum level and stays there until the perihelion is reached.

    Then the May perihelion causes a temporary rise, in this case 106 in May and 137 in June. After that follows the low period, far lower than the predicted 140-160. In this case the quiet period reaches the maximum time, which causes the maximum in 2000 to be far lower (some 110) than the general prediction has been.

    If we look back the 250 years that we have more or less reliable figures, what is mystifying in the Sun's behavior in 1998-2000? If we look back the 2000 years that has been estimated from undirect sources, we have still less to wonder about. The Sun really is variable, but still obeys some strict rules.

    What is happening in the Sun is a change to a new mode: the Gleissberg cycle has reached its minimum (71 years) and now there will be a reversal to longer and lower cycles. When the 200-year cycle is also nearing its turning point (2010-2030), my theory also predicts a turn of the global warming to a global chill. The warm winters of 1990's correlate very well with the highest smoothed sunspot activity since at least 1700's, and probable since 1200's. But that's another story.

    Another interesting paper by NASA was titled "The Day the Solar Wind Disappeared" (science.nasa.gov/newhome/headlines/ast13dec99_1.htm). I quote: "From May 10-12, 1999, the solar wind that blows constantly from the Sun virtually disappeared -- the most drastic and longest-lasting decrease ever observed." ... "Starting late on May 10 and continuing through the early hours of May 12, NASA's ACE and Wind spacecraft each observed that the density of the solar wind dropped by more than 98%." ... "According to observations from the ACE spacecraft, the density of helium in the solar wind dropped to less than 0.1% of its normal value, and heavier ions, held back by the Sun's gravity, apparently could not escape from the Sun at all."

    According to NGDC, the Wolf sunspot number got a jump a few days earlier: 08 May the number was 151 and 09 May it was 149, when the first-May value was 75 and the peak was followed by a decrease, so that the value was 85 in May 24. Compare these to the smoothed value of May, 90.

    According to my theory the Jupiter's perihelion very much regulates the sunspot cycles. The last Jovian perihelion occurred just during those days in May 1999, when the Sun appeared to behave abnormally. But the effect does not include only those few days, it affects the whole cycle.


    1.3. The relation of the length of the cycle to its magnitude

    Besides the length there are other variables that characterize the sunspot cycles, especially the magnitude or intensity of the cycle. The oldest and still the most common way to measure it is to calculate the so called sunspot number. The sunspot number is derived from the equation R=k(f+10G), where f is the number of spots, G is the number of spot groups and k is a factor of the observer that depends e.g. on the type and size of the telescope used plus the opacity of the sky, the so-called seeing. The timing of the minimum was not based on any theory, and so is the case also with this number. Nevertheless, it is the only choice available in this kind of study that penetrates centuries, because the availability of the results with alternate methods are at most 50 years. It's accuracy is debatable but for our purposes it is enough. The situation can be improved by using smoothed and average values as is commonly done and as I will also mostly do.

    Until the year 1980 the values were gathered in Zurich. Today the international values are handled by National Geophysical Data Center in Boulder, Colorado. The values are originally counted in Belgium based on several tens of observation stations.

    Besides these so-called Wolf numbers, named so after the developer of this method, a widely used value is the 10.7 centimeter (2800 Mhz) radio flux. It tells the energy of the sun as fractions of Joule per time, area and frequency interval. The frequency interval of 2800 MHz is adjusted to 1 Astronomical Unit. Originally the measurements were made at Ottawa, today they are measured in British Columbia. The correlation between this flux and the Wolf number is astoundingly good on both monthly and yearly basis. The main reason this study uses Wolf instead of the flux is that we have monthly Wolf numbers since 1749, but flux numbers only from 1947. We can't afford to lose 200 years. And besides 50 years are too short a time period for this analysis.

    I begin with a table containing 1. the number of the cycle, 2. the year of the minimum, 3. the year of the naximum, 4. the length of the cycle, 5. the period from minimum to maximum, and 6. the maximum sunspot number based on the 13-month smoothed averages.

    TABLE 12. THE MAGNITUDE AND THE RISE PERIOD TO MAXIMUM.

    1.     2.   3.   4.  5.  6.   
         
     1 1755.2 1961 11.3 6.3  87       
     2 1766.5 1769  9.0 3.2 116      
     3 1775.5 1778  9.2 2.9 159      
     4 1784.7 1788 13.6 3.4 141       
     5 1798.3 1805 12.1 6.7  49 maximum is 17 years after the preceding 
     6 1810.4 1816 12.9 6.0  49 (record low with the preceding one)     
     7 1823.3 1829 10.6 6.6  72      
     8 1833.9 1837  9.6 3.3 147 maximum is 7 years after the preceding 
     9 1843.5 1848 12.5 4.6 132      
    10 1856.0 1860 11.2 4.1  98      
    11 1867.2 1870 11.7 3.4 141      
    12 1878.9 1883 10.7 5.0  75      
    13 1889.6 1894 12.1 4.5  88      
    14 1901.7 1907 11.9 5.3  64      
    15 1913.6 1917 10.0 4.0 105      
    16 1923.6 1928 10.2 4.8  78      
    17 1933.8 1937 10.4 3.6 119      
    18 1944.2 1947 10.1 3.3 152      
    19 1954.3 1957 10.4 3.7 201 (record high)      
    20 1964.9 1968 11.8 4.7 111      
    21 1976.5 1979 10.3 3.4 165      
    22 1986.8 1989  9.8 2.8 159 
    23 1996.4 2000>12.8?4.0 121 length predicted 
    24(2009?  2014           30-60)prediction
    

    ***************************************************************

    As one can see from the table, the rise to maximum is not symmetrical with the fall from it. Only 3 of the 22 rises exceed 50% or 6 years of the total cycle length. These begin the cycles 1, 5 and 7. Cycles 1 and 7 precede 9-year cycles, cycle 5 is the other of the two lowest cycles since 1750. Besides these the cycles 6, 12, 14 and 16 are nearly symmetrical, time of rise being about 45% of the total. The cycle 6 is the other record-low cycle and the other three cycles are the coming, middle and leaving ones as regards the minimum standstill when the Jovian intersects the Sun's plane. The rest or 15 of the 22 cycles are clearly asymmetrical the time of rise being typically about one third of the total time or 3.5 years with the ten year type cycle. The average of all the 22 cycles is 4.4 years or very nearly 40 % of the total time.

    In the following analysis the smoothed Wolfian magnitude maximum is denoted R(M).

    TABLE 13. R(M) compared with the time of rise to maximum

    length of rise 2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 years 
    R(M)
     40- 59                                        XX 
     60- 79                        X       XX      X  
     80- 99                        XX              X
    100-119                XX      XX 
    120-139                        X
    140-159        XX      XXXX  
    160-179                X 
    180-199
    200-219                X 
    

    ***************************************************************

    Regression analysis:

    If Y = sunspot number and X = length of rise, then

    Y = 236-28X

    correlation = -0.82
    s.d.=40

    **************************************************************

    CONCLUSION 7. THE MAXIMUM POSSIBLE SUNSPOT NUMBER

    If there were no time of rise, the maximum sunspot number would be 236, which can thus be regarded as the theoretical upper limit (the highest empirically observed sunspot number is the 201 of the cycle 19).

    **************************************************************

    Every year added will lower the maximum sunspot number with 28 Wolfs: Correspondingly the maximum rise of time would be 7.1 years (the empirical record is the 6.7 years of the low cycle 5, which ended with the spotless year 1810). So we have:

    risetime R(M)

    3yrs 151
    4yrs 124
    5yrs 96
    6yrs 68
    7yrs 41

    First of all, we can make three remarks. The maximum of the first of the two lowest cycles or 5, is 17 years after the previous maximum, which is an all-time record (since 1750). The highest known cycle or the cycle 19 had its maximum at the aphelion. The spotless minimum, that follows the Jovian cycle 5, begins its nearly two years long period of spotless months exactly at the perihelion.

    Besides these there is one more feature that is interesting. If one classifies the residuals (the real value of R(M) minus the theoretical value), we get the following grouping (two points to the exact risetime and one point to the previous and the following because of the inaccuracy):

    TABLE 14. The residuals of the actual maximum magnitude compared with the theoretical value

                                         xxxxxx 
                                         xxxxxxxxx      xxx  
                                         xxxxxxxxx   xxxxxx
                       xxx            xxxxxxxxxxxxxxxxxxxxxxxx   xxx
                    xxxxxxxxx         xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    
    deviation(Wolfs)-31-30-29-28-27-26-25-24-23-22-21-20-19-18-17-16-15
    
    Gap 1 (-14...-2)
    
                        xxxx
                        xxxx
                        xxxx
                        xxxxxx        xxxx
                      xxxxxxxxxxxxxxxxxxxx
                      xxxxxxxxxxxxxxxxxxxxxx
    deviation (Wolfs) -1 0 1 2 3 4 5 6 7 8 9
    
    Gap 2 (10...19)
                              
                                 xxxxxx
                         xxx      xxxxxxxxxxxx  
                      xxxxxxxxxxxxxxxxxxxxxxxxxxx
    
    deviation (Wolfs)  20 21 22 23 24 25 26 27 28   
    
    Gap 3 (29...67)
    
                         xxx 
                      xxxxxxxxx
     
    deviation (Wolfs)  68 69 70
    

    *************************************************************

    So we have residuals about -24...-23, 0...1, 24-25 and about 69. Could the residuals be -24, 0, 24, 48 and 72 (possibly also -72) and what could cause this period of 24 Wolfs? I have no answer to this question, but because this is a statistical study, I try to catch every regularity, even if I have no explanation.

    Click here to get to PART 2.

    CONTENTS

    - Average sunspot magnitude during 19 Jovian years 1762-1987.
    - Is the Jovian effect real or an artifact?
    - How many Jovian years are needed for the effect to show up?

    Click here to get to PART 3.

    CONTENTS

    - Magnitude minima.
    - Magnitude maxima.
    - Medians and quartiles.
    - The perihelian stability.

    Click here to get to PART 4.

    CONTENTS

    - How long is the 11-year cycle?
    - The rules of Schove interpreted.
    -- The supercycle of 7 consecutive cycles.
    -- The supercycle of 14 consecutive cycles.
    - The Precambrian Elatina formation.
    - The Gleissberg cycle.

    Click here to get to PART 5.

    CONTENTS

    - A 2000-year historical perspective.
    -- The Roman Empire and its demise.
    -- The Mayan Classic Period.
    -- When the Nile froze in 829 AD.
    -- Why is it Iceland and Greenland and not vice versa?
    -- Tambora did not cause it.
    -- The spotless century 200 AD.
    -- The recent warming caused by Sun.
    -- The 200-year weather pattern.
    - An autocorrelation analysis.
    -- Three variants of 200 years.
    -- The basic cycle length.
    -- The Gleissberg cycle put into place.
    - 200-year cyclicity and a temperature correlation.
    - The periods of Cole.

    Click here to get to PART 6.

    CONTENTS

    - Smoothing sunspot averages in 1768-1992 by one sunspot cycle.
    - Smoothing by the Hale cycle.
    - Smoothing by the Gleissberg cycle.
    - Double smoothing.
    - Omitting minima or taking into account only the active parts of the cycle.

    Click here to get to PART 7.

    CONTENTS

    - Summary of supercycles and a hypercycle of 2289 years.
    --- Short supercycles.
    --- Supercycles from 250 years to a hypercycle of 2289 years.
    --- The long-range change in magnitudes.
    --- Stuiver-Braziunas analysis: 9000 years?

    Click here to get to PART 8.

    CONTENTS

    - Organizing the cycles into a web.

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